<div class="csl-bib-body">
<div class="csl-entry">Di Fratta, G., Pfeiler, C.-M., Praetorius, D., & Ruggeri, M. (2023). The Mass-Lumped Midpoint Scheme for Computational Micromagnetics: Newton Linearization and Application to Magnetic Skyrmion Dynamics. <i>Computational Methods in Applied Mathematics</i>, <i>23</i>(1), 145–175. https://doi.org/10.1515/cmam-2022-0060</div>
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dc.identifier.issn
1609-4840
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/153587
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dc.description.abstract
We discuss a mass-lumped midpoint scheme for the numerical approximation of the Landau-Lifshitz-Gilbert equation, which models the dynamics of the magnetization in ferromagnetic materials. In addition to the classical micromagnetic field contributions, our setting covers the non-standard Dzyaloshinskii-Moriya interaction, which is the essential ingredient for the enucleation and stabilization of magnetic skyrmions. Our analysis also includes the inexact solution of the arising nonlinear systems, for which we discuss both a constraint preserving fixed-point solver from the literature and a novel approach based on the Newton method. We numerically compare the two linearization techniques and show that the Newton solver leads to a considerably lower number of nonlinear iterations. Moreover, in a numerical study on magnetic skyrmions, we demonstrate that, for magnetization dynamics that are very sensitive to energy perturbations, the midpoint scheme, due to its conservation properties, is superior to the dissipative tangent plane schemes from the literature.
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dc.description.sponsorship
FWF - Österr. Wissenschaftsfonds
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dc.language.iso
en
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dc.publisher
De Gruyter
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dc.relation.ispartof
Computational Methods in Applied Mathematics
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dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
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dc.subject
Landau–Lifshitz–Gilbert equation
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dc.subject
Dzyaloshinskii–Moriya Interaction
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dc.subject
Magnetic skyrmions
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dc.subject
Newton Linearization
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dc.subject
Computational Micromagnetics
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dc.subject
Finite Elements
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dc.title
The Mass-Lumped Midpoint Scheme for Computational Micromagnetics: Newton Linearization and Application to Magnetic Skyrmion Dynamics